You get me intrigued with this

I actually believe that wavelets are the way to go for such things,
but, besides that anything beyond a Haar wavelet is too complicated for me
(and I just grasp that Haar very superficially of course),

I think one problem is the problem you mentioned - don't do anything with the bands,
only then you have perfect reconstruction

And what to do you do with the bands to make a pitch shift or to preserve formants/do some vocoding?

It's not so obvious (to me), my naive idea I mentioned earlier in this thread was to
do short FFTs on the bands and manipulate the FFTs only

But how? if you time stretch them, I believe the pitch goes down (thats my intuition only, I am not sure)
and also, these bands alias, since the filters are not brickwall,
and the aliasing is only canceled on reconstruction I believe?

So, yes, very interesting topic, that could lead me astray for another couple of weeks but without any results I guess

I think as long as I don't fully graps all the properties of the FFT and phase vocoder I shouldn't start anything new...

Am 09.11.2018 um 22:31 schrieb robert bristow-johnson:

what you're discussing here appears to me to be about perfect reconstruction in the context of Wavelets and Filter Banks.

there is a theorem that's pretty easy to prove that if you have complementary high and low filterbanks with a common cutoff at 1/2 Nyquist, you can downsample both high and low-pass filterbank outputs by a factor of 1/2 and later combine the two down-sampled streams of samples to get perfect reconstruction of the original.  this result is not guaranteed if you **do** anything to either filter output in the filterbank.

---------------------------- Original Message ----------------------------
Subject: Re: [music-dsp] 2-point DFT Matrix for subbands Re: FFT for realtime synthesis?
From: "gm" <>
Date: Fri, November 9, 2018 4:19 pm
> hm, my application has also WOLA ...
> All I find is about up- and downsampling of time sequences and spectra
> of the same length.

> If anyone knows of an easy explanation of down- and up sampling spectra
> it would be much appreciated.
> Am 09.11.2018 um 19:16 schrieb Ethan Duni:
> ..
>> The only applications I know of that tolerate time-domain aliasing in
>> transforms are WOLA filter banks - which are explicitly designed to
>> cancel these (severe!) artifacts in the surrounding time-domain
>> processing.


r b-j               

"Imagination is more important than knowledge."

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